# Linear Programming-Graphical Method and Simplex Method of Solutions [Optionals IAS Mains Mathematics]: Questions 1 - 7 of 11

Access detailed explanations (illustrated with images and videos) to **283** questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. *Unlimited Access, Unlimited Time, on Unlimited Devices*!

View Sample Explanation or View Features.

Rs. 750.00 -OR-

How to register? Already Subscribed?

## Question 1

Appeared in Year: *2016*

### Describe in Detail

Essay▾Find the maximum value of with constrains , , by graphical method. [CS (Main) Paper 2]

### Explanation

- Given with constrains , ,
- For graph, we convert the inequalities into equation.
and

- In equation
If

- Then
Point is

If

- Then
point is

- In equation
- If then
Point is

- If then
Point is

- Plotting these equations on the graph. Area of in the figure satisfied by the constraint is shown by the shaded area and is called…

… (56 more words) …

## Question 2

Appeared in Year: *2016*

### Describe in Detail

Essay▾Maximize subject to is the optional solution unique justify your answer. [CS (Main) Paper 2]

### Explanation

- After introducing slack variable in the constraint, we convert inequalities into equalities, and assign coefficient to slack variable in the objective function. The resultant objective function and constraint equation are given below.
Subject to

- The table for simplex computation are shown below.
- Since all the elements of Cj-Zj row are or zero, so w…

… (51 more words) …

## Question 3

Appeared in Year: *2012*

### Describe in Detail

Essay▾For each hour per day that Ashok studies mathematics, it yields him 10 marks and for each hour that he studies physics, it yields him 5 marks. He can study at most 14 hours a day and he must get at least 40 marks in each. Determine graphically how many hours a day he should study mathematics and physics each, in order to maximize his marks? (CS paper -2)

### Explanation

Let be the number of hour he study mathematics and y be the number of hour he study physics

Max (marks function)

Subject to

Where

Now, in order to plot the graph, we convert the inequalities into equation.

… eq. (i)

And

… eq. (ii)

And 3) … eq. (iii)

Any Combination of value of x and y which satisfies the given constr…

… (69 more words) …

## Question 4

Appeared in Year: *2007*

### Describe in Detail

Essay▾Solve the following by simplex method

Maximize

Subject to

(CS paper -2)

### Explanation

Given problem is

Maximize

Subject to

We introduce slack variables and convert constraints into equation and assign ‘o’ co-efficient to the slack variables in the objective function.

Max

Subject to

Simplex Table 1

Simplex Table 2

Simplex Table 3

Simplex Table 4

Since all

So optimal solution is obtained

… (41 more words) …

## Question 5

Appeared in Year: *2013*

### Describe in Detail

Essay▾Minimize

Subject to the constraints

(CS paper -2)

### Explanation

Given

Minimize

Maximize

Subject to the constraints

Table 1

Table 2

Table 3

Since all the values of

So optimal solution obtained

… (35 more words) …

## Question 6

Appeared in Year: *2013*

### Describe in Detail

Essay▾Maximize

Subjected to

And (CS paper -2)

### Explanation

Given max

Subjected to

And

We introduce surplus and artificial variable and assign O co-efficient to surplus to artificial variable. The resultant objective function and constraint are given as under:

Max

Where

Table 1

Table 2

Table 3

Since all the values of

So optimal solution obtained

… (35 more words) …

## Question 7

Appeared in Year: *2011*

### Describe in Detail

Essay▾Solve by simplex method, the following LP problem:

Maximize,

Constraints,

(CS paper -2)

### Explanation

Given

Maximize,

Constraints,

We introduce slack variables and convert constraints into equation and assign ‘o’

Coefficient to the slack variable in the objective function

Max

Subject to

Where

Simplex Table 1

Simplex Table 2

Simplex Table 3

Since all the

So optimal solution obtained

Max

… (21 more words) …